Final answer:
The water tank weighs 2,370 pounds when filled; after subtracting the tank's empty weight of 501 pounds, the water's weight is 1,869 pounds. Using the conversion factor that 1 gallon of water weighs approximately 8.34 pounds, the calculation shows that the tank would contain 224 gallons of water. However, since the tank's capacity is 177 gallons, the actual amount of water in the tank is 177 gallons.
Step-by-step explanation:
We have a water tank that weighs 501 pounds when empty and with water added, its total weight is 2,370 pounds. To calculate the weight of the water alone, we need to subtract the empty tank weight from the total weight:
Weight of water = Total weight - Empty tank weight
Weight of water = 2,370 pounds - 501 pounds
Weight of water = 1,869 pounds
Now, we need to convert the weight of the water to gallons. We know that 1 gallon of water weighs approximately 8.34 pounds. Therefore, to find out how many gallons we have, we divide the weight of the water by the weight per gallon:
Gallons of water = Weight of water / Weight per gallon
Gallons of water = 1,869 pounds / 8.34 pounds/gallon
Gallons of water = 224.22 gallons
Since a tank cannot contain a fractional amount of liquid, we can infer that the tank contains 224 gallons of water assuming the closest whole number. However, this initial calculation did not account for the tank's capacity, so we must also consider that the maximum capacity of the tank is 177 gallons. Therefore, 177 gallons of water are in the tank.